Estimating scale economies in non-convex production models

The literature on nonparametric frontier technologies lacks a method for the measurement of scale economies in non-convex settings. This paper proposes a general procedure which is based on the minimization of the ray average cost and requires the solution of a single programming problem. Our approach allows for multiple optima to introduce the case of global sub-constant scale economies, and it also permits the estimation of scale economies at a local level. The empirical application investigates the role of replicability and the relationship between global and local indicators. It also points out the managerial implications for companies operating in the Italian public transit industry.     

中国上市建筑企业规模经济和范围经济评价——一种随机边界成本函数方法

目前对于企业规模经济和范围经济的研究大多数是在不存在X无效的假设下进行的。即认为企业始终是在它们的有效边界内的,因此对企业规模经济和范围经济的实证研究也都是X有效的前提下的。本文试图采用一种成本非有效的随机边界成本函数,建立广义超越对数成本函数模型对企业规模经济和范围经济进行评价。数据来源于深沪两市建筑业板块25家上市公司2003-2007年的年度报告。研究结果表明:我国上市建筑企业中同时存在着规模不经济和范围不经济,而不存在X无效性假设条件下的估计结果使得规模经济值被提高。     

Technical efficiency and economies of scale in state owned enterprises: The Hellenic telecommunications organisation

In this paper we propose methodologies for assessing the relative efficiency of state owned enterprises that operate under monopolistic conditions. Irrespective of the ownership structure (private or public) monopolistic operation is often given unclear/conflicting operating objectives by their principals or regulators and thus efficiency should be assessed using alternative objectives such as cost, production and revenue. On the methodological side the paper employs parametric functional forms using ordinary least squares and goal programming methods of estimation. A secondary estimation stage was also pursued with the input/output variables of the models being corrected for technical inefficiency. The methodology was applied to examine the technical efficiency and economies of scale of the Hellenic telecommunications organisation over the period 1971–1993.     

Supply chain design considering economies of scale and transport frequencies

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

Mean and bold? On separating merger economies from structural efficiency gains in the drinking water sector

The Dutch drinking water sector experienced two drastic changes over the last 10 years. Firstly, the sector association started a voluntary benchmarking aimed to increase the efficiency and effectiveness of the sector. Secondly, merger activity arose. This paper develops a nonparametric model to dissect and distinguish the effects on efficiency of these evolutions. Parametric corrected ordinarily least squares (Fourier) tests show the robustness of the model with respect to the specification and its variables. Although detecting an efficiency enhancing effect of benchmarking, we find insignificant merger economies due to the absence of scale economies and the absence of increased incentives to fight inefficiencies.     

Distribution of cost and profit efficiency: Evidence from Indian banking

This paper uses the nonparametric DEA methodology to estimate cost and profit efficiency of Indian banks during the post-reform period. The results show considerable variation in average levels of profit efficiency across various ownership categories of banks. In general, state owned banks are found to be more efficient than their private counter parts. Further, efficiency tends to be low among the small banks (assets up to Rs. 50 billion), indicating that at the existing scale of operations, these banks are operating far below the efficient frontier. We also examine the distribution of efficiency using nonparametric kernel density estimates. The analysis reveals a rightward-shift of the efficiency distribution over the years. A major part of this shift comes from the state owned banks. Based on the conditional distribution, the study finds strong evidence of ownership explaining the efficiency differential of banks. Additionally, bank size and product-mix are also found to be important, although to a lesser extent.     

Designing performance incentives, an international benchmark study in the water sector

Cross-country comparisons avoid the unsteady equilibrium in which regulators have to balance between economies of scale and a sufficient number of remaining comparable utilities. By the use of data envelopment analysis, we compare the efficiency of the drinking water sector in the Netherlands, England and Wales, Australia, Portugal and Belgium. After introducing a procedure to measure the homogeneity of an industry, robust order-m partial frontiers are used to detect outlying observations. By applying bootstrapping algorithms, bias-corrected first and second stage results are estimated. Our results suggest that incentive regulation in the sense of regulatory and benchmark incentive schemes have a significant positive effect on efficiency. By suitably adapting the conditional efficiency measures of Daraio and Simar (Advanced robust and nonparametric methods in efficiency analysis. Springer, New York 2007) to the bias corrected estimates of Simar and Wilson (Manage Sci, 44(1): 49–61, 1998), we incorporate environmental variables directly into the efficiency estimates. We firstly equalize the social, physical and institutional environment, and secondly, deduce the effect of incentive schemes on utilities as they would work under similar conditions. The analysis demonstrates that in absence of clear and structural incentives the average efficiency of the utilities falls in comparison with utilities which are encouraged by incentives.     

Nonparametric estimation of returns to scale in the public sector with an application to the provision of educational services

Nonparametric programming models have been developed to measure technical efficiency and scale economies. The programming models used for public sector applications, however, are based on standard private sector production theory. In the public sector environmental variables have a significant impact on the provision of public services. Without controlling for these environmental factors point estimates of efficiency and returns to scale will be biased. This paper extends nonparametric methods to allow measurement of returns to scale in the provision of public services. The method is applied to the provision of educational services in New York State school districts for illustrative purposes.     

Accounting for economies of scope in performance evaluations of university professors

Teaching and research are widely regarded as the two key activities of academics. We propose a tailored version of the popular Data Envelopment Analysis methodology to evaluate the overall performance of university faculty. The methodology enables accounting for the potential presence of economies of scope between the teaching and research activities. It is illustrated with a dataset of professors working at a Business and Administration department of a university college. The estimation results reveal that overall the performance scores of faculty decrease if we allow for spillovers from research to teaching and vice-versa.     

Location of slaughterhouses under economies of scale

The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale.We present an approach based on linearization of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.     

Productivity change in the water industry in England and Wales: application of the meta-Malmquist index

This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the meta-Malmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data.     

Long term capacity decisions in uncertain markets for advanced manufacturing systems incorporating scope economies

By examining the literature in the field of manufacturing flexibility many researchers have located several form of flexibility by distinguishing them into strategic and operational flexibility forms. Furthermore, many measures and design methods have been proposed for flexible manufacturing systems. Surely scope economies are one of the most important strategic form of flexibility in manufacturing systems and their strategic impact has been acknowledged by the very beginning of the flexible manufacturing era. However, despite several researches are available to address scope economies measurement and design methodologies, very few researches investigate their economic convenience in front of dedicated manufacturing systems depending on the competitive market conditions.This paper proposes a theoretical model whose main aim is the general understanding of the convenience conditions of scope economies-based manufacturing systems. The results of the theoretical model are very interesting, because they locate market conditions that make scope economies manufacturing systems less profitable than dedicated manufacturing ones; moreover, the proposed model sets some general criteria to guide the entrepreneur in making right investment decision regarding this kind of manufacturing investments. Such results can explain the reason of many failures of flexible manufacturing systems and it suggests the use of this kind of approach to investigate other flexibility forms of manufacturing systems. The ultimate goal of this research is the construction of a Decision Support System for supporting the entrepreneur in making decision on Advanced Manufacturing Systems investment decisions.     

Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation

Isotonic nonparametric least squares (INLS) is a regression method for estimating a monotonic function by fitting a step function to data. In the literature of frontier estimation, the free disposal hull (FDH) method is similarly based on the minimal assumption of monotonicity. In this paper, we link these two separately developed nonparametric methods by showing that FDH is a sign-constrained variant of INLS. We also discuss the connections to related methods such as data envelopment analysis (DEA) and convex nonparametric least squares (CNLS). Further, we examine alternative ways of applying isotonic regression to frontier estimation, analogous to corrected and modified ordinary least squares (COLS/MOLS) methods known in the parametric stream of frontier literature. We find that INLS is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings. In the absence of noise, the corrected INLS (CINLS) has a higher discriminating power than FDH. In the case of noisy data, we propose to apply the method of non-convex stochastic envelopment of data (non-convex StoNED), which disentangles inefficiency from noise based on the skewness of the INLS residuals. The proposed methods are illustrated by means of simulated examples.     

A robust nonparametric approach to evaluate and explain the performance of mutual funds

The topic of the measurement of mutual funds’ performance is receiving an increasing interest both from an applied and a theoretical perspective. Beside the traditional financial literature, a growing body of studies has started to apply the tools of frontier analysis for benchmarking comparisons in portfolio analysis. Our paper contributes to this literature proposing a robust nonparametric approach for analysing mutual funds. It is based on the concept of order-m frontier [Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric frontier estimation: A robust approach. Journal of Econometrics 106, 1–25] and on a probabilistic approach [Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric frontier models: A probabilistic approach. Journal of Productivity Analysis 24 (1), 93–121] to find out the factors explaining mutual funds’ performance. Within this framework, a decomposition of conditional efficiency is proposed, and its usefulness for economic interpretation analysed. Our approach is illustrated by using US mutual funds data, grouped for category by objective. Economies of scale, slacks and market risks are investigated. A comparison of traditional, nonparametric and robust performance measures is also offered.     

Regional concentration and efficiency in Mexican manufacturing

This paper explores the link between industrial location, concentration, and economic efficiency in Mexican manufacturing. Using a linear programming approach, the authors calculate indices of overall, technical, allocative, and scale efficiency for Mexican manufacturing industries by state to test whether, in 1985, those regions with high levels of industrial concentration were suffering from the costs of congestion. The evidence suggests that, at least at the aggregate level, there continued to be a positive relationship between industry concentration and efficiency in production. There is also evidence that overall efficiency was related to scale efficiency, although highly industrialized regions on the production frontier often operated at inefficient scales. In particular, the most concentrated regions (the Federal District, the state of Mexico, Jalisco, and Nuevo León) consistently display decreasing returns to scale, indicating that the process of industrial concentration may be leading to diseconomies of scale. Finally, an econometric analysis suggests that scale, urbanization, and agglomeration economies are positively related to overall and technical efficiency at the regional level, while foreign ownership is negatively related. Agglomeration economies at the industry level were not significant. The paper also makes a methodological contribution. It is the first application of a distance-function production methodology to measuring regional efficiency in a developing country. It demonstrates how to conduct distance-function efficiency analysis using the newly developed GAMS mathematical programming environment. These tools should be of considerable interest to applied microeconomists.     

Technical efficiency and economies of scale: A non-parametric analysis of REIT operating efficiency

This study measures technical efficiency and economies of scale for real estate investment trusts (REITs) by employing data envelopment analysis (DEA), a linear-programming technique. Using data from the National Association of Real Estate Investment Trusts (NAREITs) for the years 1992–1996, we find that REITs are technically inefficient, and the inefficiencies are a result of both poor input utilization and failure to operate at constant returns to scale. With respect to scale inefficiency, most REITs are operating at increasing returns to scale, suggesting that REITs could improve performance through expansion. Moreover, we employ regression analysis to determine what characteristics influence the efficiency measures obtained. The results show that internal REIT management is positively related to all measures of efficiency. Increasing leverage is negatively related to REIT input utilization. Finally, increasing REIT diversification across property types enhances scale efficiency (SE) but reduces input usage efficiency.     

Specialization, inequality and the social stability of economies with collective property rights

Many, if not most, economies are observed to exhibit some form of collective ownership with some goods. These economies may fail to be socially stable, in the sense that the economy has an empty core; some groups may have an incentive to ‘recontract out’. We show that, for a class of economies with collective ownership, sufficient ‘specialization’ in the endowment holdings of these economies gives rise to a non-empty core, so achieving social stability. It is shown, moreover, that reductions in income inequality are consistent with social stability, to the extent that these reductions preserve or increase ‘specialization’ in the economy. Finally, we show that our notion of specialization is not limited to the privatized sector of the economy. Even in economies in which there is no privately held property, sufficient specialization guarantees that the economy is socially stable.     

Fast Nonparametric Quantile Regression With Arbitrary Smoothing Methods

The calculation of nonparametric quantile regression curve estimates is often computationally intensive, as typically an expensive nonlinear optimization problem is involved. This article proposes a fast and easy-to-implement method for computing such estimates. The main idea is to approximate the costly nonlinear optimization by a sequence of well-studied penalized least squares-type nonparametric mean regression estimation problems. The new method can be paired with different nonparametric smoothing methods and can also be applied to higher dimensional settings. Therefore, it provides a unified framework for computing different types of nonparametric quantile regression estimates, and it also greatly broadens the scope of the applicability of quantile regression methodology. This wide applicability and the practical performance of the proposed method are illustrated with smoothing spline and wavelet curve estimators, for both uni- and bivariate settings. Results from numerical experiments suggest that estimates obtained from the proposed method are superior to many competitors. This article has supplementary material online.     

Transport economies of scale and firm location

This paper studies the impact of economies of scale in transportation on a firm’s location decision. We relate the location problem to weighted Fermat problems and ramified optimal transportation problems and analyze how transport technologies affect the firm’s transportation and location choices. It is found that in general when the level of transport economies of scale is high, the firm locates its factory in the interior of the Weber triangle with a branching transport structure. Two examples are constructed to illustrate how interactions between transport technology and production technology would affect the firm’s input purchase and factory location.